D'Inverno Problem 19.10 Stationary Limit

Given that the nature of a surface is given by the sign of g(i)(i) and for the Boyer-Lindquist form of the Kerr solution g11 = -Δ/ρ2, then surely any surface of constant r where r > r+ will have a negative value for g11, so how can S+ be timelike?

Also on page 259, just below equation (19.70), he says "These curves are not geodesics, but are the world-lines of photons initially constrained to orbit with fixed r and θ. " How do you constrain photons?